What you need to know:
- Declan Rice forced a good save from Ederson as West Ham threatened late on but substitute Fernandinho made it 2-0 to City in the closing minutes.
- Manuel Lanzini pulled one back but it was not enough for David Moyes's team to avoid a second successive defeat.
Manchester City beat West Ham 2-1 in swirling snow on Sunday to return to second in the Premier League and Watford manager Claudio Ranieri endured a miserable return to Leicester.
Free-scoring Liverpool laid down the gauntlet by hammering Southampton 4-0 the previous day to move to within one point of leaders Chelsea, who host Manchester United in Sunday's late kick-off.
But reigning champions City stayed in close touch with victory at home to high-flying West Ham as the Premier League increasingly resembles a three-horse race.
Riyad Mahrez had a strike ruled out for offside at the Etihad but the hosts eventually claimed the lead shortly after the half-hour mark when a Mahrez ball into the box was deflected into the path of Ilkay Gundogan, handing the German a simple finish.
Declan Rice forced a good save from Ederson as West Ham threatened late on but substitute Fernandinho made it 2-0 to City in the closing minutes.
Manuel Lanzini pulled one back but it was not enough for David Moyes's team to avoid a second successive defeat.
Leicester's Jamie Vardy reminded Ranieri of his enduring quality even in his mid-30s, scoring twice at the King Power Stadium in a 4-2 win against Watford.
Ranieri, who famously won the Premier League title with unfancied Leicester in 2016, received a rapturous reception on his emotional first return to the stadium as an opposition manager since leaving the club early the following year.
Midfielder James Maddison gave Leicester an early lead when he capitalised on a mistake by William Troost-Ekong, only for Josh King to level from the penalty spot in the 30th minute after Wilfred Ndidi brought down Emmanuel Dennis in the area.
Leicester regained the lead four minutes later when Vardy lifted the ball over goalkeeper Daniel Bachmann from an angle and the former England striker grabbed his second three minutes before the break when he glanced in Maddison's corner.
Dennis pulled a goal back just after the hour when he robbed Timothy Castagne to race through and chip over Kasper Schmeichel but Ademola Lookman scored from close range to restore the home side's two-goal cushion.
Brentford heaped the pressure on Rafael Benitez by beating Everton 1-0 to secure their first Premier League win since early October, courtesy of a first-half penalty from Ivan Toney.
Everton have now taken just two points from their past seven league matches and are sinking fast.
The game between Burnley and Tottenham was called off a little under an hour before kick-off because of heavy snow at Turf Moor in northwest England.
Attempts to clear the pitch proved in vain as the undersoil heating struggled to cope and snow fell as quickly as it could be removed.
Cristiano Ronaldo had to settle for a place on the bench as temporary Manchester United boss Michael Carrick made four changes to their starting XI to face Chelsea at Stamford Bridge.